Re: Muon paradox

On 4/15/2025 10:10 PM, Paul.B.Andersen wrote:

Den 10.04.2025 22:02, skrev Aether Regained:

Paul.B.Andersen:

>
The speed of muons is v = ~ 0.999668⋅c through the atmosphere
which also is within the laboratory with open roof.
γ = 38.8.
>
The mean proper lifetime of a muon is t₀ = 2.2 μs.
But measured in the Earth's rest frame the lifetime of the muon
is  tₑ = 2.2e-6⋅γ s = 85.36 μs (time dilation!).
>
Since muons are created at a height ~15 km, and the time for
a muon to reach the earth is t = 15e3/v = 5.005 s,
then the part of the muon flux that will reach the Earth is
  N/N₀ = exp(-t/tₑ) = 0.556, so 55.6% of the muons would reach the Earth.
>
If the lifetime of the muons had been 2.2 μs, then the part of
the muon flux that will reach the Earth would be:
  N/N₀ = exp(-t/t₀) = 1.32e-10.
So only 0.0000000132% of the muons would reach the Earth.
>
Can you guess which of them is closest to what is observed?
>

>
@PaulBAndersen
>
There is one flaw I find in the SR explanation, can you confirm if it is
true:
>
What is really measured are these (the facts):
>
1. The mean proper lifetime of a muon is t₀ = 2.2 μs.
2. muons are created at a height ~15 km
3. The speed of the muons is ~c, so travel time is ~50.05 μs
4. muon flux measured on the Earth's surface is about 55.6% of what it
is at 15km.
>
 From 1, 2 and 3, the expected muon flux on the Earth's surface is:
>
N/N₀ = exp(-t/t₀) = exp(-50.05/2.2) = 1.32e-10 = 0.0000000132%
>
The important point (the flaw) is that the speed of the muon has not
actually been measured to be 0.999668⋅c, but instead is computed.
>
N/N₀ = exp(-t/γt₀) = .556 => γ = 38.8 => v = 0.999668⋅c
>
The SR explanation would have been more convincing, if the speed had
actually been measured to that many significant figures.

 Nothing but the mean lifetime is really measured in my scenario above.

In your scenario? Sure. Most  or the
"measurements" invoked by relativistic
idiots are imagined; real measurements
of course are t'=t, you're even stupid
enough to admit it.